There are great expectations when it comes to kids’ birthday parties these days: themes (“Frozen,” anyone?), elaborate cakes, and activities like karaoke. Gone are the days of Pin the Tail on the Donkey. Most parents don’t wince at party planning—initially. But by the time of the party, they’re often too stressed or tired to enjoy the festivities. There are plenty of ways to make these events simpler and more enjoyable for everyone, including mom and dad. One of the most challenging issues is cleanup. It must be done, but once the party’s over, you just want to put your feet...